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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 11

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 11

Define a \(\Delta \)-complex structure on the Klein bottle \(K\) and use it to compute \(H_*(K;\mathbb {Z})\), \(H_*(K;\mathbb {Z}_2)\), and \(H_*(K;\mathbb {Q})\).

Raw LaTeX

Define a \(\Delta\)-complex structure on the Klein bottle \(K\) and use it to compute
\(H_*(K;\mathbb{Z})\), \(H_*(K;\mathbb{Z}_2)\), and \(H_*(K;\mathbb{Q})\).

Topic Tags

Homology with Coefficients Surface Topology and Surface Groups